
are of interest.
Therefore, a natural question arising here
is how to derive the solutions of FL
from the solutions of (REF ).
From the modern mathematical point of view, the algebro-geometric solutions of FL\(_{\pm }\)  hierarchy
can be more or less solved if the formulas
(REF ) and () are derived.
However, this correspondence is only formal to some extent and needs
further
analysis about the parameters in the solutions (REF ) and ().
As remark in [1]}, the one-soliton of AKNS system, depends on four complex
parameters \(a,b,\phi ,\psi .\)  Setting
\(\ell (x,t)=\exp \left(ax+f_0(a)t+\phi \right),\quad m(x,t)=\exp \left(bx-f_0(-b)t+\psi \right),\) 
